Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-06-12
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages. accepted by Communications in theoretical physics (Beijing)
Scientific paper
Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.
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